System resource component utilization

ABSTRACT

A computer implemented method including receiving a set of utilization metrics for a system comprising at least an average number of concurrent requests to the system and a maximum concurrency that the system is capable of supporting, providing a function that incorporates two curve segments, computing a utilization according to a ratio of the average concurrent requests to the function, and managing performance problems indicated by the utilization. A computer implemented method including receiving a set of response time metrics comprising at least an average response time, average concurrent requests, and a minimum interference response time, computing a current response ratio of the minimum interference response time and the average response time, computing a maximum response ratio corresponding to a maximum concurrency, determining the maximum concurrency is inaccurate by comparing the maximum response ratio and the current response ratio, and replacing the maximum concurrency.

BACKGROUND OF THE INVENTION

The present invention relates generally to the field of system resourceutilization, and more specifically to computing a set of utilizationmetrics.

With respect to computer systems, utilization refers to a system's usageof processing resources, or the amount of available resources beingutilized to execute a current workload. Actual utilization variesdepending on the amount and type of managed computing tasks. Certaintasks may require intense system utilization, while others may requiresignificantly less, such as may be the case when part of a task isallocated to resources outside of the system. In some cases, utilizationmay be used to gauge a system's performance. For example, a heavyutilization with only a few running programs may indicate insufficientpower support to a system, or running programs hidden by a systemmonitor. The latter may be a high indicator of viruses or malwarepresent on the system. For these reasons, a utilization is a usefulmetric for analyzing system performance.

SUMMARY

As disclosed herein, a computer implemented method for computing asystem utilization includes receiving a set of utilization metrics for asystem comprising at least an average number of concurrent requests tothe system Nand a maximum concurrency c that the system is capable ofsupporting, providing a function FixP_(D)(N) that incorporates two curvesegments that form a smooth joint at a point at which they intersect,computing a utilization U according to a ratio of the average concurrentrequests N to the function FixP_(D)(N), and managing performanceproblems indicated by the utilization. A computer program productcorresponding to the method is also disclosed.

Also disclosed herein, a computer implemented method for adjusting asystem's maximum concurrency include receiving a set of response timemetrics comprising at least an average response time R, averageconcurrent requests N, and a minimum interference response time s,computing a current response ratio M of minimum interference responsetime s and average response time R, computing a maximum response ratioK(c) corresponding to a maximum concurrency c, determining maximumconcurrency c is inaccurate by comparing maximum response ratio K(c) andcurrent response ratio M, and responsive to determining maximumconcurrency c is inaccurate, replacing maximum concurrency c withaverage concurrent requests N.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a block diagram depicting one embodiment of a utilizationmonitoring system in accordance with some embodiments of the presentinvention;

FIG. 2 is a flowchart depicting one embodiment of a utilizationcalculation method in accordance with some embodiments of the presentinvention;

FIG. 3 is a flowchart depicting a maximum concurrency adjustment methodin accordance with some embodiments of the present invention;

FIG. 4 is a flowchart depicting one embodiment of a tipping pointcalculation method in accordance with some embodiments of the presentinvention;

FIG. 5 depicts a block diagram of components of a computer, inaccordance with some embodiments of the present invention.

DETAILED DESCRIPTION

With respect to the utilization of a system, the average number ofrequests to a system N can be computed according to the equation:

N=c*U/(1-U ^(c))  (1)

With respect to equation (1), the variable c indicates a maximumconcurrency of the system, and the variable U indicates the utilizationof the system. A maximum concurrency is a maximum number of requeststhat a system is capable of handling at the same time without needing toqueue any of the work. The utilization of a system refers to thefraction of available resources being utilized. In some cases, theaverage number of requests to a system may be easier to monitor than theutilization of the system. In such cases, it may be beneficial to beable to compute the utilization with respect to the average number ofrequests and the maximum concurrency. Rearranging equation 1 yields:

U=N/(N+c*(1−U)/(1-U ^(c)))  (2)

Equation (2) describes the utilization U in terms of itself, thereforethe solution is a value of U that is invariant with respect to theoperation shown on the right hand side. Equations such as this aredescribed as fixed-point equations. The fixed-point operation thatappears on the right-hand side of equation (2) has the desirableproperty that any guess as to the value of U can be improved by applyingit. However, the improvement may not occur rapidly enough for thisapproach to be useful for computing a utilization. Also of note, thedenominator of equation 2 lies within a certain range that is dependenton N, making it possible to model the denominator based on N. For thesereasons, computing the utilization can be simplified by replacing thedenominator of equation 2 with an empirical approximation based on N,hereinafter referred to as FixP_(D)(N) A system and method for computinga utilization using such an empirical approximation is described hereinwith respect to the following figures.

FIG. 1 is a block diagram depicting components of a utilizationmonitoring system 100 in accordance with some embodiments of the presentinvention. As depicted, utilization monitoring system 100 includesresource monitor 110, utilization calculator 120, and applications 130Aand 130B. Utilization monitoring system 100 is an example of anenvironment in which utilization calculation may be utilized.

Resource monitor 110 may be configured to monitor metrics associatedwith a computer system's utilization. In some embodiments, resourcemonitor 110 is configured to monitor the utilization of multipleapplications within utilization monitoring system 100 to provide anaggregated utilization metric. Resource monitor 110 may be configured tomonitor the utilization of utilization monitoring system 100 in itsentirety. In other embodiments, resource monitor 110 is configured tomonitor the utilization of an application of interest, such asapplication 130A or 130B, within utilization monitoring system 100. Theutilization metrics monitored by resource monitor 110 may include amaximum concurrency c that utilization monitoring system 100 is capableof supporting. In some embodiments, resource monitor 110 is configuredto execute a concurrency calculation method such as concurrencycalculation method 300 discussed with respect to FIG. 3. In someembodiments, the utilization metrics monitored by resource monitor 110also includes an observed average number of concurrent requests N on thesystem. Utilization metrics 115 may be provided to utilizationcalculator 120.

Utilization calculator 120 may be configured to receiver utilizationmetrics 115 from resource monitor 110. In some embodiments, utilizationcalculator 120 is configured to execute a utilization calculationmethod, such as utilization calculation method 200 described withrespect to FIG. 2, to provide a utilization corresponding to computersystem 100. Additionally, utilization calculator 120 may be configuredto compute a tipping point corresponding to the average number ofconcurrent requests Non the system. Utilization calculator 120 may beconfigured to provide the utilization to a user or to anotherapplication.

Applications 130A and 130B may be representative of any applicationsalso existing within utilization monitoring system 100. The depictedembodiment shows only two applications, but it should be appreciatedthat there may be any number of applications on utilization monitoringsystem 100. In some embodiments, one application of interest, such asapplication 130A, may be monitored by resource monitor 110. In saidembodiments, utilization calculator 120 receives utilization metrics 115corresponding to application 130A and computes a utilizationcorresponding to application 130A alone. In another embodiment, multipleapplications, such as applications 130A and 130B, may be monitored byresource monitor 110. In said embodiments, utilization calculator 120receives utilization metrics 115 corresponding to applications 130A and130B and computes a utilization corresponding to applications 130A and130B considered as one unit.

FIG. 2 is a flowchart depicting a utilization calculation method 200 inaccordance with some embodiments of the present invention. As depicted,utilization calculation method 200 includes receiving (210) a set ofutilization metrics, computing (230) a tipping point p corresponding toan average number of concurrent requests, providing (240) a functionFixP_(D)(N), computing (250) a utilization U, and managing (260)performance problems indicated by the utilization U. Utilizationcalculation method 200 may enable a utilization to be computedaccurately within two decimal places.

Receiving (210) a set of utilization metrics may include receivingstatistics relevant to the utilization of a system. In some embodiments,the set of utilization metrics includes a maximum concurrency c that acomputing system is capable of supporting. The set of utilizationmetrics may also include an observed average number of concurrentrequests N on the system. In some embodiments, the set of utilizationmetrics includes an average measured response time of the system R aswell as a response time s for requests issued when the current number ofoutstanding requests was less than the estimated concurrency by at leastone request. In one embodiment, the received set of utilization metricsmay correspond to one or more applications of interest within a system.

Adjusting (220) maximum concurrency c may include executing a maximumconcurrency adjustment method. In one embodiment, the executed maximumconcurrency adjustment method corresponds to maximum concurrencyadjustment method 300 as described with respect to FIG. 3. Adjusting(220) maximum concurrency c may provide a more accurate maximumconcurrency c, and may therefore enable a more accurate utilizationcalculation.

Computing (230) a tipping point corresponding to an average number ofconcurrent requests may include processing the received set ofutilization metrics to provide a tipping point p. In some embodiments,computing (230) a tipping point may include executing a tipping pointcalculation method such as tipping point calculation method 400discussed with respect to FIG. 4.

Providing (240) a function FixP_(D)(N) may include providing a functionof the maximum concurrency c, the tipping point p, and the averagenumber of concurrent requests N. FixP_(D)(N) is an approximation for thedenominator of equation (1). The denominator of equation 1 exhibits abehavior in which there are two ranges. Each range responds to changesin N differently, but the pattern of response can be described within agiven range. For this reason, the function FixP_(D)(N) may be apiecewise function or a non-piecewise function. In one embodiment, thefunction FixP_(D)(N) is a function that incorporates two curve segmentsthat form a smooth joint at the point at which they meet. In someembodiments, the function FixP_(D)(N) may also be a function that has anoverall smooth shape. For example, the function FixP_(D)(N) may bedefined as:

FixP_(D)(N)=c+f(f(N/p)) if N<p

FixP_(D)(N)=N+1+b*f(p/N) if N≥p

where f(y)=y−b*y*(1−y)+0.5*b*(b−1)*y*(1−y)²  (3)

With respect to equation 3, the variable b is defined as b=c−p. Equation3 meets all of the criteria as previously defined; that is, it is apiecewise function that incorporates two curve segments that form asmooth joint at the point at which they meet. The function also has ashape that could be classified as smooth.

Computing (250) a utilization U may include processing the functionFixP_(D)(N) corresponding to the received maximum concurrency c, theaverage number of concurrent requests N, and the computed tipping pointp. The utilization U may then be computed with respect to the functionFixP_(D)(N) and the average number of concurrent requests N. In oneembodiment, the utilization U is computed according to the equation:

U=N/FixP_(D)(N)  (4)

Computing the utilization U via equation 4 may provide a utilizationthat is accurate with a precision of two digits. One additionaladvantage of using equation (3) and equation (4) to compute theutilization is that the calculations required by equation (3) andequation (4) do not require the use of transcendental mathematicaloperations. Therefore, processing environments that support only fouroperation arithmetic are capable of executing this calculation method.

Managing (260) performance problems indicated by the utilization U mayinclude analyzing the utilization U to determine if the system orindividual components of the system are being over-utilized. In oneembodiment, managing (260) performance problems indicated by theutilization includes identifying components of the system that exhibit ahigh utilization and adjusting the system to balance the utilizationacross available components. Additionally, adjusting the system couldinclude introducing additional components to the system to help balancethe workload more efficiently.

FIG. 3 is a flowchart depicting a maximum concurrency adjustment method300 in accordance with some embodiments of the present invention. Asdepicted, the maximum concurrency adjustment method 300 includesreceiving (310) response time metrics, computing (320) a currentresponse ratio, computing (330) a maximum concurrency response ratioK(c) for when the number of active requests is equal to maximumconcurrency c, determining (340) if M is less than K(c), determining(350) if the average number of requests N is less than maximumconcurrency c, determining (360) if N is greater than maximumconcurrency c, confirming (370) maximum concurrency c, and replacing(380) maximum concurrency c. Maximum concurrency adjustment method 300may enable the maximum concurrency of a system to be monitored anddynamically adjusted.

Receiving (310) response time metrics may include receiving statisticscorresponding to the time it takes a system to respond to a request. Insome embodiments, receiving (310) response time metrics includesreceiving an average measured response time R. Receiving (310) responsetime metrics may also include receiving a minimum interference responsetime s corresponding to requests issued when the current number ofoutstanding requests was at least one request below the estimatedconcurrency.

Computing (320) a current response ratio may include determining a ratioof the minimum interference response time to the average measuredresponse time. In some embodiments, the response ratio M is computedaccording to the equation:

M=s/R  (5)

Response ratio M corresponds only to a time period for which themeasured values s and R are applicable.

Computing (330) a maximum concurrency response ratio K(c) for when thenumber of active requests is equal to maximum concurrency c may includeproviding a function K(c) for estimating a response ratio for differentvalues of c. In one embodiment, the function may be:

K(c)=c/(c+1+0.6875*b+0.3125*b/c+0.5*b ² /c ²)  (6)

With respect to equation 4, the variable b is defined as b=c−p. Equation6 may be utilized to compute a response ratio for any number of valuesof maximum concurrency c.

Determining (340) if M is less than K(c) may include comparing thecurrent response ratio M to the maximum concurrency response ratio K(c).If it is determined that current response ratio M is less than maximumconcurrency response ratio K(c) (340, yes branch), the method continuesby determining (350) if the average number of requests N is less thanmaximum concurrency c. If it is determined that current response ratio Mis not less than maximum concurrency response ratio K(c) (340, nobranch), the method continues by determining if the average number ofrequests N is greater than the maximum concurrency c.

Determining (350) if the average number of requests N is less thanmaximum concurrency c may include comparing the average number ofrequests N to the current maximum concurrency c. If it is determinedthat the average number of requests N is less than maximum concurrency c(350, yes branch), the method continues by replacing (380) maximumconcurrency c. If it is determined that the average number of requests Nis not less than maximum concurrency c (350, no branch), the methodcontinues by confirming (370) maximum concurrency c.

Determining (360) if the average number of requests N is greater thanmaximum concurrency c may include comparing the average number ofrequests N to the current maximum concurrency c. If it is determinedthat the average number of requests N is greater than the maximumconcurrency c (360, yes branch), the method continues by replacing (380)maximum concurrency c. If it is determined, that the average number ofrequests N is less than the maximum concurrency c (360, no branch), themethod continues by confirming (370) maximum concurrency c.

Confirming (370) maximum concurrency c may include leaving the currentvalue of maximum concurrency c unaltered. If the method reaches thisstep, it has been determined that there is no reason to believe that cis an inaccurate measurement of the maximum concurrency, and thereforeadjustments need not be made. In some embodiments, confirming (370) themaximum concurrency of the system is c includes terminating the methodwithout making any adjustments to the maximum concurrency c.

Replacing (380) maximum concurrency c may include redefining the valuec. If the method reaches this step, it has been determined that there isreason to believe that the value c may be an inaccurate measurement ofthe maximum concurrency, and therefore adjustments should be made. Inone embodiment, replacing maximum concurrency c comprises redefining cto be equivalent to the current average number of requests N. Thisprocedure is performed because at this step, there is reason to believethat the value of N lies between the inaccurate concurrency measurementc and the true maximum concurrency of the system.

FIG. 4 is a flowchart depicting a tipping point calculation method 400in accordance with some embodiments of the present invention. Asdepicted, tipping point calculation method 400 includes receiving (410)maximum concurrency c, computing (420) a distance D between maximumconcurrency c and a nearest integer d, computing (430) a harmonic numbercorresponding to maximum concurrency c, and computing (440) a tippingpoint according to maximum concurrency c.

Receiving (410) maximum concurrency c may include receiving a metricindicating a maximum number of concurrent requests a system is capableof supporting. In one embodiment, the maximum concurrency c correspondsto an entire computer system. In other embodiments, the maximumconcurrency c corresponds to one or more applications of interest.

Computing (420) a distance between maximum concurrency c and a nearestinteger d may include identifying an integer d that is closest tomaximum concurrency c. Once d is identified, an absolute distance Dbetween c and d is computed according to the equation D=|c−d|. DistanceD may be utilized to compute a harmonic number corresponding to maximumconcurrency c.

Computing (430) a harmonic number corresponding to maximum concurrency cmay include utilizing a provided equation to compute an extendedharmonic number G(c). In one embodiment, G(c) is computed according tothe equation:

G(c)=2*D*{H _([c+1])−1/(2[c]+2.52)}+(1-2*D)*H _(d)  (7)

With respect to equation 7, the notation [c] corresponds to the greatestinteger function of c. That is, for non-negative numbers, [c] is theinteger part of c. Additionally, the notation Ha corresponds to thed^(th) harmonic number in the set of harmonic numbers.

Computing (440) a tipping point may include processing extended harmonicnumber G(c) and maximum concurrency c to provide a tipping point p. Inone embodiment, the tipping point p is computed according to theequation:

p=c−G(c+2)+G(3)+1.6/(c+7)−9.6/(c+47)  (8)

When equation 8 is utilized to compute the tipping point p, equation 7must first be utilized to compute G(c+2). The tipping point p may beutilized in a utilization calculation method such as utilizationcalculation method 200 as an input variable for computing a utilization.

While equation (3) and equation (4) may enable utilization calculationfor processors that support only four operation arithmetic, theutilization may be computed directly by repeated application of equation(2) in processing environments that enable transcendental mathematicaloperations. In such environments, the utilization may also be calculatedas follows:

U _(i+1) =U _(i)−(c*U _(i) +N*U _(i) ^(c) −N)*c/(c ² +N ²) for N≤p

U _(i+1)=[U _(i) ^(c)−(c*U _(i) +N*U _(i) ^(c) −N)*N/(c ² +N ²)]^(1/c)for N>p

where U ₀ =N/(c+v ^((c+1)/2)) for N≤p

U ₀ =N/(N+1+b*v ^(√((c+1)/2))) for N>p  (9)

With respect to equation (9), i=0, 1, 2 . . . etc., v=min(N,p)/max(N,p),and the other variables are as previously defined. U can be estimated tobe any member of the sequence formed by equation 9.

FIG. 5 depicts a block diagram of components of computer 500 inaccordance with an illustrative embodiment of the present invention. Itshould be appreciated that FIG. 5 provides only an illustration of oneimplementation and does not imply any limitations with regard to theenvironments in which different embodiments may be implemented. Manymodifications to the depicted environment may be made.

As depicted, the computer 500 includes communications fabric 502, whichprovides communications between computer processor(s) 504, memory 506,persistent storage 508, communications unit 512, and input/output (I/O)interface(s) 514. Communications fabric 502 can be implemented with anyarchitecture designed for passing data and/or control informationbetween processors (such as microprocessors, communications and networkprocessors, etc.), system memory, peripheral devices, and any otherhardware components within a system. For example, communications fabric502 can be implemented with one or more buses.

Memory 506 and persistent storage 508 are computer-readable storagemedia. In this embodiment, memory 506 includes random access memory(RAM) 516 and cache memory 518. In general, memory 506 can include anysuitable volatile or non-volatile computer-readable storage media.

One or more programs may be stored in persistent storage 508 for accessand/or execution by one or more of the respective computer processors504 via one or more memories of memory 506. In this embodiment,persistent storage 508 includes a magnetic hard disk drive.Alternatively, or in addition to a magnetic hard disk drive, persistentstorage 508 can include a solid state hard drive, a semiconductorstorage device, read-only memory (ROM), erasable programmable read-onlymemory (EPROM), flash memory, or any other computer-readable storagemedia that is capable of storing program instructions or digitalinformation.

The media used by persistent storage 508 may also be removable. Forexample, a removable hard drive may be used for persistent storage 508.Other examples include optical and magnetic disks, thumb drives, andsmart cards that are inserted into a drive for transfer onto anothercomputer-readable storage medium that is also part of persistent storage508.

Communications unit 512, in these examples, provides for communicationswith other data processing systems or devices. In these examples,communications unit 512 includes one or more network interface cards.Communications unit 512 may provide communications through the use ofeither or both physical and wireless communications links.

I/O interface(s) 514 allows for input and output of data with otherdevices that may be connected to computer 500. For example, I/Ointerface 514 may provide a connection to external devices 520 such as akeyboard, keypad, a touch screen, and/or some other suitable inputdevice. External devices 520 can also include portable computer-readablestorage media such as, for example, thumb drives, portable optical ormagnetic disks, and memory cards. Software and data used to practiceembodiments of the present invention can be stored on such portablecomputer-readable storage media and can be loaded onto persistentstorage 508 via I/O interface(s) 514. I/O interface(s) 514 also connectto a display 522.

Display 522 provides a mechanism to display data to a user and may be,for example, a computer monitor.

The programs described herein are identified based upon the applicationfor which they are implemented in a specific embodiment of theinvention. However, it should be appreciated that any particular programnomenclature herein is used merely for convenience, and thus theinvention should not be limited to use solely in any specificapplication identified and/or implied by such nomenclature.

The flowchart and block diagrams in the Figures illustrate thearchitecture, functionality, and operation of possible implementationsof systems, methods and computer program products according to variousembodiments of the present invention. In this regard, each block in theflowchart or block diagrams may represent a module, segment, or portionof code, which comprises one or more executable instructions forimplementing the specified logical function(s). It should also be notedthat, in some alternative implementations, the functions noted in theblock may occur out of the order noted in the figures. For example, twoblocks shown in succession may, in fact, be executed substantiallyconcurrently, or the blocks may sometimes be executed in the reverseorder, depending upon the functionality involved. It will also be notedthat each block of the block diagrams and/or flowchart illustration, andcombinations of blocks in the block diagrams and/or flowchartillustration, can be implemented by special purpose hardware-basedsystems that perform the specified functions or acts, or combinations ofspecial purpose hardware and computer instructions.

The present invention may be a system, a method, and/or a computerprogram product. The computer program product may include a computerreadable storage medium (or media) having computer readable programinstructions thereon for causing a processor to carry out aspects of thepresent invention.

The computer readable storage medium can be a tangible device that canretain and store instructions for use by an instruction executiondevice. The computer readable storage medium may be, for example, but isnot limited to, an electronic storage device, a magnetic storage device,an optical storage device, an electromagnetic storage device, asemiconductor storage device, or any suitable combination of theforegoing. A non-exhaustive list of more specific examples of thecomputer readable storage medium includes the following: a portablecomputer diskette, a hard disk, a random access memory (RAM), aread-only memory (ROM), an erasable programmable read-only memory (EPROMor Flash memory), a static random access memory (SRAM), a portablecompact disc read-only memory (CD-ROM), a digital versatile disk (DVD),a memory stick, a floppy disk, a mechanically encoded device such aspunch-cards or raised structures in a groove having instructionsrecorded thereon, and any suitable combination of the foregoing. Acomputer readable storage medium, as used herein, is not to be construedas being transitory signals per se, such as radio waves or other freelypropagating electromagnetic waves, electromagnetic waves propagatingthrough a waveguide or other transmission media (e.g., light pulsespassing through a fiber-optic cable), or electrical signals transmittedthrough a wire.

Computer readable program instructions described herein can bedownloaded to respective computing/processing devices from a computerreadable storage medium or to an external computer or external storagedevice via a network, for example, the Internet, a local area network, awide area network and/or a wireless network. The network may comprisecopper transmission cables, optical transmission fibers, wirelesstransmission, routers, firewalls, switches, gateway computers and/oredge servers. A network adapter card or network interface in eachcomputing/processing device receives computer readable programinstructions from the network and forwards the computer readable programinstructions for storage in a computer readable storage medium withinthe respective computing/processing device.

Computer readable program instructions for carrying out operations ofthe present invention may be assembler instructions,instruction-set-architecture (ISA) instructions, machine instructions,machine dependent instructions, microcode, firmware instructions,state-setting data, or either source code or object code written in anycombination of one or more programming languages, including an objectoriented programming language such as Smalltalk, C++ or the like, andconventional procedural programming languages, such as the “C”programming language or similar programming languages. The computerreadable program instructions may execute entirely on the user'scomputer, partly on the user's computer, as a stand-alone softwarepackage, partly on the user's computer and partly on a remote computeror entirely on the remote computer or server. In the latter scenario,the remote computer may be connected to the user's computer through anytype of network, including a local area network (LAN) or a wide areanetwork (WAN), or the connection may be made to an external computer(for example, through the Internet using an Internet Service Provider).In some embodiments, electronic circuitry including, for example,programmable logic circuitry, field-programmable gate arrays (FPGA), orprogrammable logic arrays (PLA) may execute the computer readableprogram instructions by utilizing state information of the computerreadable program instructions to personalize the electronic circuitry,in order to perform aspects of the present invention.

Aspects of the present invention are described herein with reference toflowchart illustrations and/or block diagrams of methods, apparatus(systems), and computer program products according to embodiments of theinvention. It will be understood that each block of the flowchartillustrations and/or block diagrams, and combinations of blocks in theflowchart illustrations and/or block diagrams, can be implemented bycomputer readable program instructions.

These computer readable program instructions may be provided to aprocessor of a general purpose computer, special purpose computer, orother programmable data processing apparatus to produce a machine, suchthat the instructions, which execute via the processor of the computeror other programmable data processing apparatus, create means forimplementing the functions/acts specified in the flowchart and/or blockdiagram block or blocks. These computer readable program instructionsmay also be stored in a computer readable storage medium that can directa computer, a programmable data processing apparatus, and/or otherdevices to function in a particular manner, such that the computerreadable storage medium having instructions stored therein comprises anarticle of manufacture including instructions which implement aspects ofthe function/act specified in the flowchart and/or block diagram blockor blocks.

The computer readable program instructions may also be loaded onto acomputer, other programmable data processing apparatus, or other deviceto cause a series of operational steps to be performed on the computer,other programmable apparatus or other device to produce a computerimplemented process, such that the instructions which execute on thecomputer, other programmable apparatus, or other device implement thefunctions/acts specified in the flowchart and/or block diagram block orblocks.

The descriptions of the various embodiments of the present inventionhave been presented for purposes of illustration, but are not intendedto be exhaustive or limited to the embodiments disclosed. Manymodifications and variations will be apparent to those of ordinary skillin the art without departing from the scope and spirit of the invention.The terminology used herein was chosen to best explain the principles ofthe embodiment, the practical application or technical improvement overtechnologies found in the marketplace, or to enable others of ordinaryskill in the art to understand the embodiments disclosed herein.

What is claimed is:
 1. A computer implemented method for computing asystem utilization, the method comprising: receiving, by one or moreprocessors, a set of utilization metrics for the system comprising atleast an average number of concurrent requests to the system N and amaximum concurrency c that the system is capable of supporting;providing, by one or more processors, a function FixP_(D)(N) thatincorporates two curve segments that form a smooth joint at a point atwhich they intersect; computing, by one or more processors, autilization U according to a ratio of the average concurrent requests Nto the function FixP_(D)(N); and managing, by one or more processors,performance problems indicated by the utilization.
 2. The method ofclaim 1, further comprising computing, by one or more processors, atipping point p corresponding to the average concurrent requests N. 3.The method of claim 2, further comprising computing, by one or moreprocessors, an extended harmonic number G(c) according to the equationG(c)=2*D{H_([c+1])−1/(2*[c]+2.52)}+(1-2*D)*H_(d), wherein d is adistance between c and a nearest integer d, H_(d) is a d^(th) harmonicnumber, and [c] denotes the greatest integer function of c.
 4. Themethod of claim 3, wherein the tipping point p is computed according tothe equation p=c−G(c+2)+G(3)+1.6/(c+7)−9.6/(c+47).
 5. The method ofclaim 2, wherein the function FixP_(D)(N) is defined in terms of theaverage number of concurrent requests N, the maximum concurrency c, andthe tipping point p.
 6. The method of claim 2, wherein the providedfunction FixP_(D)(N) is defined as:FixP_(D)(N)=c+f(f(N/p)) for N<p,FixP_(D)(N)=N+1+b*f(p/N) for N≥p,wherein b=c−p and f(y)=y−b*y*(1−y)+0.5*b*(b−1)*y*(1−y)².
 7. The methodof claim 1, wherein managing performance problems indicated by theutilization U comprises: identifying, by one or more processors,components of the system that exhibit a high utilization; and adjusting,by one or more processors, the system to balance the utilization acrossavailable components.
 8. A computer implemented method for adjusting amaximum concurrency, the method comprising: receiving, by one or moreprocessors, a set of response time metrics comprising at least anaverage response time R, average concurrent requests N, and a minimuminterference response time s; computing, by one or more processors, acurrent response ratio M of minimum interference response time s andaverage response time R; computing, by one or more processors, a maximumresponse ratio K(c) corresponding to a maximum concurrency c;determining, by one or more processors, maximum concurrency c isinaccurate by comparing maximum response ratio K(c) and current responseratio M; and responsive to determining maximum concurrency c isinaccurate, replacing, by one or more processors, maximum concurrency cwith average concurrent requests N.
 9. The method of claim 8, whereindetermining maximum concurrency c is inaccurate further comprisesdetermining, by one or more processors, if M<K(c).
 10. The method ofclaim 9, further comprising: responsive to determining M is less thanK(c), determining, by one or more processors, whether average concurrentrequests N is less than maximum concurrency c.
 11. The method of claim10, further comprising: responsive to determining N is not less than c,replacing, by one or more processors, maximum concurrency c with averageconcurrent requests N.
 12. The method of claim 9, further comprising:responsive to determining M is not less than K(c), determining, by oneor more processors, whether average concurrent requests N is greaterthan maximum concurrency c.
 13. The method of claim 12, furthercomprising: responsive to determining N is not greater than c,replacing, by one or more processors, maximum concurrency c with averageconcurrent requests N.
 14. A computer program product for computing asystem utilization, the computer program product comprising: one or morecomputer readable storage media and program instructions stored on theone or more computer readable storage media, the program instructions,executable by a computer, comprising instructions to: receive, by one ormore processors, a set of utilization metrics for a system comprising atleast an average number of concurrent requests to the system N and amaximum concurrency c that the system is capable of supporting; provide,by one or more processors, a function FixP_(D)(N) that incorporates twocurve segments that form a smooth joint at a point at which theyintersect; compute, by one or more processors, a utilization U accordingto a ratio of the average concurrent requests N to the functionFixP_(D)(N); and manage, by one or more processors, performance problemsindicated by the utilization.
 15. The computer program product of claim14, further comprising program instructions to compute, by one or moreprocessors, a tipping point p corresponding to the average concurrentrequests N.
 16. The computer program product of claim 15, furthercomprising program instructions to compute an extended harmonic numberG(c) according to the equationG(c)=2*D{H_([c+1])−1/2*[c]+2.52)}+(1-2*D)*H_(d), wherein D is a distancebetween c and a nearest integer d, H_(d) is a d^(th) harmonic number,and [c] denotes the greatest integer function of c.
 17. The computerprogram product of claim 16, wherein the tipping point p is computedaccording to the equation p=c−G(c+2)+G(3)+1.6/(c+7)−9.6/(c+47).
 18. Thecomputer program product of claim 15, wherein the function FixP_(D)(N)is defined in terms of the average number of concurrent requests N, themaximum concurrency c, and the tipping point p.
 19. The computer programproduct of claim 15, wherein the provided function FixP_(D)(N) isdefined as:FixP_(D)(N)=c+f(f(N/p)) for N<p,FixP_(D)(N)=N+1+b*f(p/N) for N≥p,wherein b=c−p and f(y)=y−b*y*(1−y)+0.5*b*(b−1)*y*(1−y)².
 20. Thecomputer program product of claim 14, wherein program instructions tomanage performance problems indicated by the utilization U compriseinstructions to: identify, by one or more processors, components of thesystem that exhibit a high utilization; and adjust, by one or moreprocessors, the system to balance the utilization across availablecomponents.